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A060997
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Decimal representation of continued fraction 1, 2, 3, 4, 5, 6, 7, ...
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8
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1, 4, 3, 3, 1, 2, 7, 4, 2, 6, 7, 2, 2, 3, 1, 1, 7, 5, 8, 3, 1, 7, 1, 8, 3, 4, 5, 5, 7, 7, 5, 9, 9, 1, 8, 2, 0, 4, 3, 1, 5, 1, 2, 7, 6, 7, 9, 0, 5, 9, 8, 0, 5, 2, 3, 4, 3, 4, 4, 2, 8, 6, 3, 6, 3, 9, 4, 3, 0, 9, 1, 8, 3, 2, 5, 4, 1, 7, 2, 9, 0, 0, 1, 3, 6, 5, 0, 3, 7, 2, 6, 4, 3, 5, 7, 8, 6, 1, 1, 4, 6, 5, 9, 5, 0
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The value of this continued fraction is the ratio of two Bessel functions: BesselI(0,2)/BesselI(1,2) = A070910/A096789. Or, equivalently, to the ratio of the sums: sum_{n=0..inf} 1/(n!n!) and sum_{n=0..inf} n/(n!n!). - Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003
1.43312...=[1,2,3,4,5,...] = shape of a rectangle which partitions into n squares at stage n; i.e. this is an example of the match between the continued fraction of a number r and a rectangle having shape r. See A188640. [From Clark Kimberling, Apr 9 2011]
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FORMULA
| 1/A052119.
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EXAMPLE
| C=1.433127426722311758317183455775 ...
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MATHEMATICA
| RealDigits[ FromContinuedFraction[ Range[ 44]], 10, 110] [[1]]
(* Or *) RealDigits[ BesselI[0, 2] / BesselI[1, 2], 10, 110] [[1]]
(* Or *) RealDigits[ Sum[1/(n!n!), {n, 0, Infinity}] / Sum[n/(n!n!), {n, 0, Infinity}], 10, 110] [[1]]
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CROSSREFS
| Cf. A052119, A001053.
Sequence in context: A177158 A177034 A177933 * A177270 A177160 A129624
Adjacent sequences: A060994 A060995 A060996 * A060998 A060999 A061000
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KEYWORD
| cons,easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), May 14 2001
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